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Journal of Mathematical Chemistry

, Volume 26, Issue 1–3, pp 101–123 | Cite as

The heptakisoctahedral group and its relevance to carbon allotropes with negative curvature

  • A. Ceulemans
  • R.B. King
  • S.A. Bovin
  • K.M. Rogers
  • A. Troisi
  • P.W. Fowler
Article

Abstract

We introduce the pollakispolyhedral groups and describe in detail the representational structure of PSL(2,7) or 7O, the automorphism group of the Klein graph composed of 56 trivalent vertices arranged in 24 heptagonal faces. Leapfrog and quadruple transformations of the graph are described and their eigenvalue spectra derived. Considered as carbon frameworks on the “plumber's nightmare” surface these chiral structures exhibit significant steric strain which prevents the molecular realisation of the Klein symmetry.

Keywords

Fullerene Conjugacy Class Simple Group Permutation Group Rotation Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • A. Ceulemans
    • 1
  • R.B. King
    • 2
  • S.A. Bovin
    • 1
  • K.M. Rogers
    • 3
  • A. Troisi
    • 3
  • P.W. Fowler
    • 3
  1. 1.Departement ScheikundeK.U. LeuvenLeuvenBelgium
  2. 2.Department of ChemistryUniversity of GeorgiaAthensUSA
  3. 3.School of ChemistryUniversity of ExeterExeterUK

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